Q: Which of the following correctly represents the result of dividing $$ (A \times 10^x) by$$ $$ (B \times 10^y) in $$scientific notation?

$$ \frac{A}{B} \times 10$$^{x-y}$$ $$

Question 1

When multiplying two numbers in scientific notation, such as $$ (A 	imes 10^x) 	imes (B 	imes 10^y) $$, what is the correct method to determine the exponent of the result?

Accepted Answer

Add the exponents $$x$$ and $$y.$$

Question 2

Which of the following correctly represents the result of dividing $$ (A 	imes 10^x)  by$$ $$ (B 	imes 10^y)  in $$scientific notation?

Accepted Answer

$$ \frac{A}{B} 	imes 10$$^{x-y}$$ $$

Question 3

After performing multiplication or division with numbers in scientific notation, how do you determine the number of significant figures in the final answer?

Accepted Answer

Use the number with the least number of significant figures.

Question 4

Calculate $$ (2.134 	imes 10^5$) 	imes (1.6 	imes 10$$^{-3}$$) \div (3.07 	imes 10^6$) $$ and express your answer in proper scientific notation with the correct number of significant figures.

Accepted Answer

$$ 1.1 	imes 10$$^{-4}$$ $$

Question 5

A laboratory technician multiplies $$ (7.33 	imes 10^8$)  by$$ $$ (9.89 	imes 10$$^{-1}$$) $$ and then divides by $$ (6.12 	imes 10$$^{11}$$) . $$What is the answer, rounded to the correct number of significant figures?

Accepted Answer

$$ 1.18 	imes 10$$^{-3}$$ $$

Question 6

Which of the following is the correct result for $$ (4.5 	imes 10^2$) 	imes (2.0 	imes 10^3$) $$?

Accepted Answer

$$ 9.0 	imes 10^4$ $$

Question 7

A nurse needs to calculate a medication dose using $$ (3.00 	imes 10$$^{-2}$$) \div (6.0 	imes 10^1$) . $$What is the correct answer in scientific notation with the proper number of significant figures?

Accepted Answer

$$ 5.0 	imes 10$$^{-4}$$ $$

Question 8

Which operation is performed on the exponents when dividing two numbers in scientific notation?

Accepted Answer

Subtract the denominator's exponent from the numerator's exponent.

Question 9

A student calculates $$ (5.0 	imes 10^4$) \div (2.5 	imes 10^2$) . $$What is the correct answer, using the rules for significant figures?

Accepted Answer

$$ 2.0 	imes 10^2$ $$

Question 10

Which of the following best explains why $$ (1.23 	imes 10^3$) 	imes (4.56 	imes 10^2$) $$ should be reported as $$ 5.61 	imes 10^5$ $$?

Accepted Answer

The answer must have as many significant figures as the number with the least significant figures.

Question 11

A chemist multiplies $$ (6.0 	imes 10$$^{-5}$$)  by$$ $$ (3.0 	imes 10^2$) $$ and then divides by $$ (2.0 	imes 10^1$) . $$What is the final answer, with correct significant figures?

Accepted Answer

$$ 9.0 	imes 10$$^{-4}$$ $$

Question 12

If you multiply $$ (8.0 	imes 10^6$)  by$$ $$ (2.5 	imes 10$$^{-2}$$) $$, what is the correct answer in scientific notation with the proper number of significant figures?

Accepted Answer

$$ 2.0 	imes 10^5$ $$

Question 13

A solution is prepared by dividing $$ (9.00 	imes 10^3$)  by$$ $$ (3.0 	imes 10^2$) . $$What is the answer, using the correct number of significant figures?

Accepted Answer

$$ 3.0 	imes 10^1$ $$

Question 14

Which of the following is the correct result for $$ (1.5 	imes 10^2$) 	imes (2.0 	imes 10$$^{-3}$$) $$?

Accepted Answer

$$ 3.0 	imes 10$$^{-1}$$ $$

Question 15

A pharmacist needs to calculate $$ (4.00 	imes 10$$^{-2}$$) \div (8.0 	imes 10^1$) . $$What is the correct answer in scientific notation with the proper number of significant figures?

Accepted Answer

$$ 5.0 	imes 10$$^{-4}$$ $$

Question 16

Which of the following is NOT a correct step when multiplying or dividing numbers in scientific notation?

Accepted Answer

Add exponents when dividing.

Scientific Notation Operations in GOB Chemistry

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